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     "text": [
      "\u001b[32m\u001b[1m    Status\u001b[22m\u001b[39m `/mnt/E4E0A9C0E0A998F6/github/ReinforcementLearningAnIntroduction.jl/notebooks/Project.toml`\n",
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      " \u001b[90m [02c1da58]\u001b[39m\u001b[37m ReinforcementLearningAnIntroduction v0.2.0 [`..`]\u001b[39m\n",
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      " \u001b[90m [2f01184e]\u001b[39m\u001b[37m SparseArrays \u001b[39m\n"
     ]
    }
   ],
   "source": [
    "]st"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling ReinforcementLearningAnIntroduction [02c1da58-b9a1-11e8-0212-f9611b8fe936]\n",
      "└ @ Base loading.jl:1273\n"
     ]
    }
   ],
   "source": [
    "using ReinforcementLearningAnIntroduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the value estimation of the Grid World example, we create a distribution based environment model to describe the Grid World first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "const GridWorldLinearIndices = LinearIndices((5,5))\n",
    "const GridWorldCartesianIndices = CartesianIndices((5,5))\n",
    "\n",
    "function nextstep(s::CartesianIndex{2}, a::CartesianIndex{2})\n",
    "    if s == CartesianIndex(1, 2)\n",
    "        ns, r = CartesianIndex(5, 2), 10.\n",
    "    elseif s == CartesianIndex(1, 4)\n",
    "        ns, r = CartesianIndex(3, 4), 5.\n",
    "    else\n",
    "        ns = s + a\n",
    "        if 1 ≤ ns[1] ≤ 5 && 1 ≤ ns[2] ≤ 5\n",
    "            ns, r = ns, 0.\n",
    "        else\n",
    "            ns, r = s, -1.\n",
    "        end\n",
    "    end\n",
    "    [(nextstate=GridWorldLinearIndices[ns], reward=r, prob=1.0)]\n",
    "end\n",
    "\n",
    "const GridWorldActions = [CartesianIndex(-1, 0),\n",
    "                          CartesianIndex(1,0),\n",
    "                          CartesianIndex(0, 1),\n",
    "                          CartesianIndex(0, -1)]\n",
    "\n",
    "const GridWorldEnvModel = DeterministicDistributionModel([nextstep(GridWorldCartesianIndices[s], a) for s in 1:25, a in GridWorldActions]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the `GridWorldEnvModel` is an instance of `DeterministicDistributionModel`. It is used to describe the the grid world in Figure 3.2 on the book. Given a state `s` and an action `a`, we can get an Array of the probability of the reward to receive and next state. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![fig_3_2.png](img/fig_3_2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{NamedTuple{(:nextstate, :reward, :prob),Tuple{Int64,Float64,Float64}},1}:\n",
       " (nextstate = 2, reward = 0.0, prob = 1.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GridWorldEnvModel(1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_state, n_action = length(get_observation_space(GridWorldEnvModel)), length(get_action_space(GridWorldEnvModel))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create a random policy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "\n",
    "default(size=(800, 600))\n",
    "using StatsBase:sample, Weights\n",
    "\n",
    "V = TabularApproximator(n_state=n_state)\n",
    "\n",
    "policy_evaluation!(\n",
    "    V = V,\n",
    "    π=RandomPolicy(DiscreteSpace(n_action)),\n",
    "    model=GridWorldEnvModel\n",
    ")\n",
    "\n",
    "heatmap(1:5, 1:5, reshape(V.table, 5,5), yflip=true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can try the policy iteration method with a `DeterministicPolicy` policy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "V = TabularApproximator(n_state=n_state)\n",
    "policy_iteration!(;\n",
    "    V=V,\n",
    "    π=TabularDeterministicPolicy(rand(1:n_action, n_state), n_action),\n",
    "    model=GridWorldEnvModel\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heatmap(1:5, 1:5, reshape(V.table, 5,5), yflip=true)"
   ]
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